1. Parmi les sous-ensembles suivants, lesquels sont des sous-espaces vectoriels de R? U = {(r, y, z) | x – 2y + z = 0} V = {(r, xy, y) | x, y E R} W = {(x, y, 2) | 2x – 5z = 0} X = {(x+ y, Y, x - 2y) | r, y E R} %3D A. Seulement U et V B. Seulement U et W C. Seulement W et X D. Seulement U, V et W E. Seulement U, V et X F. Seulement U, W et X

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Which of the following subsets are vector subspaces of R3?
1.
Parmi les sous-ensembles suivants, lesquels sont des sous-espaces vectoriels de R3?
U = {(x, y, z) | x – 2y + z = 0}
V = {(r, ry, y) | x, y € R}
{(x, y, z) | 2x – 5z = 0}
X =
W
%3D
{(x+y, Y, x – 2y) |x, Y € R}
A. Seulement U et V
B. Seulement U et W
C. Seulement W et X
D. Seulement U, V et W
E. Seulement U, V et X
F. Seulement U, W et X
Transcribed Image Text:1. Parmi les sous-ensembles suivants, lesquels sont des sous-espaces vectoriels de R3? U = {(x, y, z) | x – 2y + z = 0} V = {(r, ry, y) | x, y € R} {(x, y, z) | 2x – 5z = 0} X = W %3D {(x+y, Y, x – 2y) |x, Y € R} A. Seulement U et V B. Seulement U et W C. Seulement W et X D. Seulement U, V et W E. Seulement U, V et X F. Seulement U, W et X
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